Number of ring structures

The curves in Figure 1 describe intramolecular reaction in irreversible, linear and non-linear random polymerisations. For linear polymerisations, theories have been developed(7,11,12) which account for the decrease in cext as a reaction proceeds and allow Nr to be calculated satisfactorily as a function of p for a given value of Pab. For non-linear polymerisations, the larger numbers of ring structures result in less adequate descriptions of Nr versus p curves using similartheories(12-17). Such theories require more development before Nr as a function of p and the gel... 

Given random reaction, the number of gel-gel pairs of groups reacting at p, i.e. the number of ring structures (loops) forming at p, is... 

Glycols may undergo intramolecular cydization or cyclically condense with other molecules to form a number of ring structures. Transesterification of carbonates with ethylene glycol produces ethylene carbonate [96 49-1] (eq. 4). Numerous materials catalyze carbonate transesterifications. 

Previous studies( ) have shown how the number fraction of ring structures formed during irreversible linear random polymerisations leading to polyurethanes may be measured. The work has been extended(7,8) to non-linear polyurethane formation using hexa-methylene diisocyanate(HDI) and POP triols. For non-linear polymerisations, it is found that the number of ring structures per molecule(Nr) is always significant, even in bulk reactions. 

Figure 1. Number of ring structure per molecule (Np) as a function of extent of reaction(p) for linear and non-linear polyurethane forming reactions in bulk with approximately equimolar concentrations of reactive groups, r =[NC0no/[pHlo = 1) (6.7).

Figure 2-36. Identification of the number of rings in adamantane after graph reduction (the different ring systems are highlighted with bold lines). Note that a graph does not car 3D information thus, the two structures on the upper right-hand side are identical.

The second step, the so called generation, created only those structures which complied with the given constraints, and imposed additional restrictions on the compounds such as the number of rings or double bonds. The third and final phase, the tester phase, examined each proposed solution for each proposed compound a mass spectrum was predicted which was then compared with the actual data of the compound. The possible solutions were then ranked depending on the deviation between the observed and the predicted mass spectra. 

In general the most stable resonance structure for a polycyclic aromatic hydro carbon is the one with the greatest number of rings that correspond to Kekule formula tions of benzene Naphthalene provides a fairly typical example... 

Although the number of ring atoms is the structural feature upon which we focus attention, we shall use the criteria of thermodynamics and kinetics to assess the feasibility of the reactions listed above. 

In valence bond terms the pyrazine ring may be represented as a resonance hybrid of a number of canonical structures (e.g. 1-4), with charge separated structures such as (3) contributing significantly, as evidenced by the polar character of the C=N bond in a number of reactions. The fusion of one or two benzene rings in quinoxaline (5) and phenazine (6) clearly increases the number of resonance structures which are available to these systems. 

Fig. 5.23. The shock-induced polarization of the indicated polymers containing benzene rings in their structure is shown to be strongly dependent on the number of rings (after Graham [82G02]).

Mention must also be made of the neat series of reactions carried out by Wieland and Neeb which led to a number of ring extended products. These are summarized by the conversion of 406 into 406a and 407. The structure of 406a was confirmed by a comparison of its... 

Formulas 42 to 44 give examples of phosphate esters related to parathion and prepared by the above methods. In some of these compounds the ethyl group has been changed, whereas in others various substituents have been introduced into the benzene ring. A number of the structures shown have been reported by the Germans (11-18). 

Figure 1. Number fraction of ring structures per molecule (Nr) as a function of extent of reaction (p) for bulk, linear, and nonlinear polyurethane-forming reactions with approximately equimolar concentrations of reactive groups (r = [NCO]J [OH]0 ss 1) (2,3). Conditions O-linear polymerization, HDI + poly(ethyleneglycol) at 70°, [NCOfo — 5.111 mol/kg, [OH], = 5.188 mol/kg number-average number of bonds in chain forming smallest ring structure (v) = 25.2, and nonlinear polymerization, HDI and POP triol at 70°C, [NCO] — 0.9073 mol/kg, [OH]0 = 0.9173 mol/kg v = 115. Reproduced with permission from Ref. 5.

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